Synopses & Reviews
This is a specialized textbook on graph factorizations, an area which lies partly in graph theory and partly in the theory of combinational designs. It is the first full-size book on its particular subject, which has previously been treated only in survey papers and in chapters in books on design theory and on graph decompositions and matching theory. The book is intended for beginning graduate students in Combinatorial Mathematics, and may be used as a text for a special topics course; but it reaches to the boundaries of current research and will also prove useful as a reference source for professionals in the field. It contains a number of easy exercises, together with some which are challenging, and a few unsolved problems. There is an extensive bibliography.
Description
Includes bibliographical references (p. 225-237) and index.
Table of Contents
List of Figures. List of Tables. Preface.
1. Graphs.
2. Walks, Paths and Cycles.
3. One-Factors and One-Factorizations.
4. Orthogonal One-Factorizations.
5. Tournament Applications of One-Factorizations.
6. A General Existence Theorem.
7. Graphs without One-Factors.
8. Edge-Colorings.
9. One-Factorizations and Triple Systems.
10. Starters.
11. Invariants of One-Factorizations.
12. Automorphisms and Asymptotic Numbers of One-Factorizations.
13. Systems of Distinct Representatives.
14. Subfactorizations and Asymptotic Numbers of One-Factorizations.
15. Cyclic One-Factorizations.
16. Perfect Factorizations.
17. One-Factorizations of Multigraphs.
18. Maximal Sets of Factors.
19. The One-Factorization Conjecture.
20. Premature Sets of Factors.
21. Cartesian Products.
22. Kotzig's Problem.
23. Other Products.
A. One-Factorizations of K
_{10}.
B. Generators of Simple Indecomposable Factorizations.
C. Generators of Nonsimple Indecomposable Factorizations. References. Index.